What I like about grammar as a subject matter is the power that it gives one to make generalizations that can be applied in a wide variety of sentences.
It does not make sense to restrict a grammatical discussion to the acceptability of a single sentence when the discussion is supposed to be about a construction.
A grammatical construction can be realized by a potentially infinite number of sentences.
Unless, as seems unlikely, do is somehow uniquely awful in this construction; if the construction is grammatical in general, it can be grammatical with do, too.
Here's another example. We may suppose that Speaker B is studying the lifestyle of people in a foreign country and is reporting to A on their weekend habits.
A: What did you find them to do on weekends?
B: I found them to go to the movies, eat meals out, and take walks in the park, just as we often do over the weekend.